Abstract

We obtain criteria for entanglement and the EPR paradox for spin-entangled particles and analyse the effects of decoherence caused by absorption and state purity errors. For a two qubit photonic state, entanglement can occur for all transmission efficiencies. In this case, the state preparation purity must be above a threshold value. However, Bohm’s spin EPR paradox can be achieved only above a critical level of loss. We calculate a required efficiency of 58%, which appears achievable with current quantum optical technologies. For a macroscopic number of particles prepared in a correlated state, spin entanglement and the EPR paradox can be demonstrated using our criteria for efficiencies η>1/3 and η>2/3 respectively. This indicates a surprising insensitivity to loss decoherence, in a macroscopic system of ultra-cold atoms or photons.

© 2009 Optical Society of America

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  1. A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
    [CrossRef]
  2. J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-201 (1965).
  3. A. Peres, "Separability Criterion for Density Matrices," Phys. Rev. Lett. 77, 1413-1415 (1996).
    [CrossRef] [PubMed]
  4. M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-State Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?," Phys. Rev. Lett. 80, 5239-5242 (1998).
    [CrossRef]
  5. K. Wooters, "Entanglement of Formation of an Arbitrary State of Two Qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).
    [CrossRef]
  6. G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002).
    [CrossRef]
  7. T. Yu and J. H. Eberly, "Sudden Death of Entanglement," Science 323, 598-601, (2009).
    [CrossRef] [PubMed]
  8. W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715-775 (2003).
    [CrossRef]
  9. T. Yu and J. H. Eberly, "Finite-Time Disentanglement Via Spontaneous Emission," Phys. Rev. Lett. 93, 140404 (2004).
    [CrossRef] [PubMed]
  10. Z. Ficek and R. Tanas, "Dark periods and revivals of entanglement in a two-qubit system," Phys. Rev. A 74, 024304 (2006).
    [CrossRef]
  11. M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
    [CrossRef] [PubMed]
  12. A. M. Steane, "Error Correcting Codes in Quantum Theory," Phys. Rev. Lett. 77, 793-797 (1996).
    [CrossRef] [PubMed]
  13. C. H. Bennett et al., "Mixed-state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
    [CrossRef] [PubMed]
  14. P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A 52, R2493- R2496 (1995).
    [CrossRef] [PubMed]
  15. D. Bohm, Quantum Theory (Englewood Cliffs, NJ, Prentice-Hall, 1951).
  16. J. Larsson, "Modeling the singlet state with local variables," Phys. Lett. A 256, 245-252 (1999).
    [CrossRef]
  17. R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model," Phys. Rev. A 40, 4277-4281 (1989).
    [CrossRef] [PubMed]
  18. M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
    [CrossRef]
  19. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
    [CrossRef] [PubMed]
  20. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, "A wavelength-tunable fiber-coupled source of narrowband entangled photons," Opt. Express 15, 15377-15386 (2007).
    [CrossRef] [PubMed]
  21. A. Garg and N. D. Mermin, "Detector inefficiencies in the Einstein-Podolsky-Rosen experiment," Phys. Rev. D 35, 3831-3835 (1987).
    [CrossRef]
  22. B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
    [CrossRef] [PubMed]
  23. P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
    [CrossRef]
  24. A. Aspect, J. Dalibard, and G. Roger, "Experimental Test of Bell’s Inequalities using Time- Varying Analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982), among others.
    [CrossRef]
  25. H. F. Hofmann and S. Takeuchi, "Violation of local uncertainty relations as a signature of entanglement," Phys. Rev. A 68, 032103 (2003).
    [CrossRef]
  26. M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
    [CrossRef] [PubMed]
  27. E. G. Cavalcanti and M. D. Reid, "Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes," J. Mod. Opt. 54, 2373-2380 (2007).
    [CrossRef]
  28. G. Toth, "Entanglement detection in optical lattices of bosonic atoms with collective measurements," Phys. Rev. A 69, 052327 (2004).
    [CrossRef]
  29. N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
    [CrossRef]
  30. W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
    [CrossRef] [PubMed]
  31. W. H. Furry, "Note on the Quantum-Mechanical Theory of Measurement," Phys. Rev. 49, 393-399 (1936).
    [CrossRef]
  32. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
    [CrossRef] [PubMed]
  33. N. D. Mermin, "Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s," Phys. Rev. D 22, 356-361 (1980).
    [CrossRef]
  34. P. D. Drummond, "Violations of Bell’s Inequality in Cooperative States," Phys. Rev. Lett. 50, 1407-1410 (1983).
    [CrossRef]
  35. M. D. Reid, W. J. Munro, and F. De Martini, "Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states," Phys. Rev. A 66, 033801 (2002).
    [CrossRef]
  36. H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Phys. Rev. Lett. 98, 140402 (2007).
    [CrossRef] [PubMed]
  37. D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
    [CrossRef] [PubMed]
  38. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
    [CrossRef] [PubMed]
  39. B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403(2001).
    [CrossRef] [PubMed]
  40. J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
    [PubMed]
  41. A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, "Conditional preparation of single photons for scalable quantum-optical networking," Phys. Rev. Lett. 93, 093601 (2004).
    [CrossRef] [PubMed]
  42. A. E. Lita, A. J. Miller, and S. W. Nam, "Counting near-infrared single-photons with 95% efficiency," Opt. Express 16, 3032-3040 (2008).
    [CrossRef] [PubMed]
  43. Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement," Opt. Express 15, 4321-4327 (2007).
    [CrossRef] [PubMed]
  44. H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
    [CrossRef] [PubMed]

2009

T. Yu and J. H. Eberly, "Sudden Death of Entanglement," Science 323, 598-601, (2009).
[CrossRef] [PubMed]

2008

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

A. E. Lita, A. J. Miller, and S. W. Nam, "Counting near-infrared single-photons with 95% efficiency," Opt. Express 16, 3032-3040 (2008).
[CrossRef] [PubMed]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

2007

Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, "Observation of -9 dB quadrature squeezing with improvement of phase stability in homodyne measurement," Opt. Express 15, 4321-4327 (2007).
[CrossRef] [PubMed]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Phys. Rev. Lett. 98, 140402 (2007).
[CrossRef] [PubMed]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, "A wavelength-tunable fiber-coupled source of narrowband entangled photons," Opt. Express 15, 15377-15386 (2007).
[CrossRef] [PubMed]

P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
[CrossRef]

E. G. Cavalcanti and M. D. Reid, "Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes," J. Mod. Opt. 54, 2373-2380 (2007).
[CrossRef]

2006

Z. Ficek and R. Tanas, "Dark periods and revivals of entanglement in a two-qubit system," Phys. Rev. A 74, 024304 (2006).
[CrossRef]

2004

T. Yu and J. H. Eberly, "Finite-Time Disentanglement Via Spontaneous Emission," Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

G. Toth, "Entanglement detection in optical lattices of bosonic atoms with collective measurements," Phys. Rev. A 69, 052327 (2004).
[CrossRef]

M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef]

A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, "Conditional preparation of single photons for scalable quantum-optical networking," Phys. Rev. Lett. 93, 093601 (2004).
[CrossRef] [PubMed]

2003

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

H. F. Hofmann and S. Takeuchi, "Violation of local uncertainty relations as a signature of entanglement," Phys. Rev. A 68, 032103 (2003).
[CrossRef]

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
[CrossRef] [PubMed]

W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715-775 (2003).
[CrossRef]

2002

G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002).
[CrossRef]

M. D. Reid, W. J. Munro, and F. De Martini, "Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states," Phys. Rev. A 66, 033801 (2002).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
[CrossRef] [PubMed]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

2001

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403(2001).
[CrossRef] [PubMed]

1999

J. Larsson, "Modeling the singlet state with local variables," Phys. Lett. A 256, 245-252 (1999).
[CrossRef]

1998

M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-State Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?," Phys. Rev. Lett. 80, 5239-5242 (1998).
[CrossRef]

K. Wooters, "Entanglement of Formation of an Arbitrary State of Two Qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).
[CrossRef]

1996

A. Peres, "Separability Criterion for Density Matrices," Phys. Rev. Lett. 77, 1413-1415 (1996).
[CrossRef] [PubMed]

A. M. Steane, "Error Correcting Codes in Quantum Theory," Phys. Rev. Lett. 77, 793-797 (1996).
[CrossRef] [PubMed]

C. H. Bennett et al., "Mixed-state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
[CrossRef] [PubMed]

1995

P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A 52, R2493- R2496 (1995).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

1989

M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
[CrossRef] [PubMed]

R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model," Phys. Rev. A 40, 4277-4281 (1989).
[CrossRef] [PubMed]

1987

A. Garg and N. D. Mermin, "Detector inefficiencies in the Einstein-Podolsky-Rosen experiment," Phys. Rev. D 35, 3831-3835 (1987).
[CrossRef]

1986

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[CrossRef] [PubMed]

1983

P. D. Drummond, "Violations of Bell’s Inequality in Cooperative States," Phys. Rev. Lett. 50, 1407-1410 (1983).
[CrossRef]

1982

A. Aspect, J. Dalibard, and G. Roger, "Experimental Test of Bell’s Inequalities using Time- Varying Analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982), among others.
[CrossRef]

1980

N. D. Mermin, "Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s," Phys. Rev. D 22, 356-361 (1980).
[CrossRef]

1965

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-201 (1965).

1936

W. H. Furry, "Note on the Quantum-Mechanical Theory of Measurement," Phys. Rev. 49, 393-399 (1936).
[CrossRef]

1935

A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Almeida, M. P.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Aspect, A.

A. Aspect, J. Dalibard, and G. Roger, "Experimental Test of Bell’s Inequalities using Time- Varying Analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982), among others.
[CrossRef]

Bachor, H.-A.

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
[CrossRef] [PubMed]

Barberi, M.

M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef]

Bell, J. S.

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-201 (1965).

Bennett, C. H.

C. H. Bennett et al., "Mixed-state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
[CrossRef] [PubMed]

Bouwmeester, D.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
[CrossRef] [PubMed]

Bowen, W. P.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
[CrossRef] [PubMed]

Bruss, D.

P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
[CrossRef]

Cavalcanti, E. G.

E. G. Cavalcanti and M. D. Reid, "Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes," J. Mod. Opt. 54, 2373-2380 (2007).
[CrossRef]

Chelkowski, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Collins, D.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Dalibard, J.

A. Aspect, J. Dalibard, and G. Roger, "Experimental Test of Bell’s Inequalities using Time- Varying Analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982), among others.
[CrossRef]

Danzmann, K.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Davidovich, L.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

De Martini, F.

M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef]

M. D. Reid, W. J. Munro, and F. De Martini, "Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states," Phys. Rev. A 66, 033801 (2002).
[CrossRef]

de Melo, F.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Di Nepi, G.

M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef]

Doherty, A. C.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Phys. Rev. Lett. 98, 140402 (2007).
[CrossRef] [PubMed]

Drummond, P. D.

P. D. Drummond, "Violations of Bell’s Inequality in Cooperative States," Phys. Rev. Lett. 50, 1407-1410 (1983).
[CrossRef]

Eberly, J. H.

T. Yu and J. H. Eberly, "Sudden Death of Entanglement," Science 323, 598-601, (2009).
[CrossRef] [PubMed]

T. Yu and J. H. Eberly, "Finite-Time Disentanglement Via Spontaneous Emission," Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

Einstein, A.

A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Esteve, J.

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

Fedrizzi, A.

Ficek, Z.

Z. Ficek and R. Tanas, "Dark periods and revivals of entanglement in a two-qubit system," Phys. Rev. A 74, 024304 (2006).
[CrossRef]

Franzen, A.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Furry, W. H.

W. H. Furry, "Note on the Quantum-Mechanical Theory of Measurement," Phys. Rev. 49, 393-399 (1936).
[CrossRef]

Furusawa, A.

Garg, A.

A. Garg and N. D. Mermin, "Detector inefficiencies in the Einstein-Podolsky-Rosen experiment," Phys. Rev. D 35, 3831-3835 (1987).
[CrossRef]

Giovanazzi, S.

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

Gisin, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Goler, S.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Gross, C.

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

Hage, B.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Herbst, T.

Hofmann, H. F.

H. F. Hofmann and S. Takeuchi, "Violation of local uncertainty relations as a signature of entanglement," Phys. Rev. A 68, 032103 (2003).
[CrossRef]

Hor-Meyll, M.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Horodecki, M.

M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-State Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?," Phys. Rev. Lett. 80, 5239-5242 (1998).
[CrossRef]

Horodecki, P.

M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-State Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?," Phys. Rev. Lett. 80, 5239-5242 (1998).
[CrossRef]

Horodecki, R.

M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-State Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?," Phys. Rev. Lett. 80, 5239-5242 (1998).
[CrossRef]

Jennewein, T.

Jones, S. J.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Phys. Rev. Lett. 98, 140402 (2007).
[CrossRef] [PubMed]

Julsgaard, B.

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403(2001).
[CrossRef] [PubMed]

Kampermann, H.

P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
[CrossRef]

Kleinmann, M.

P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
[CrossRef]

Korolkova, N.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Kozhekin, A.

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403(2001).
[CrossRef] [PubMed]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Lam, P. K.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
[CrossRef] [PubMed]

Larsson, J.

J. Larsson, "Modeling the singlet state with local variables," Phys. Lett. A 256, 245-252 (1999).
[CrossRef]

Lastzka, N.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Leuchs, G.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Linden, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Lita, A. E.

Loudon, R.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Marshall, W.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
[CrossRef] [PubMed]

Massar, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Matalon, P.

M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Mehmet, M.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Mermin, N. D.

A. Garg and N. D. Mermin, "Detector inefficiencies in the Einstein-Podolsky-Rosen experiment," Phys. Rev. D 35, 3831-3835 (1987).
[CrossRef]

N. D. Mermin, "Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s," Phys. Rev. D 22, 356-361 (1980).
[CrossRef]

Miller, A. J.

Munro, W. J.

M. D. Reid, W. J. Munro, and F. De Martini, "Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states," Phys. Rev. A 66, 033801 (2002).
[CrossRef]

Nam, S. W.

Oberthaler, M. K.

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

Penrose, R.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
[CrossRef] [PubMed]

Peres, A.

A. Peres, "Separability Criterion for Density Matrices," Phys. Rev. Lett. 77, 1413-1415 (1996).
[CrossRef] [PubMed]

Podolsky, B.

A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Polzik, E. S.

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403(2001).
[CrossRef] [PubMed]

Popescu, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Poppe, A.

Ralph, T. C.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Reid, M. D.

E. G. Cavalcanti and M. D. Reid, "Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes," J. Mod. Opt. 54, 2373-2380 (2007).
[CrossRef]

M. D. Reid, W. J. Munro, and F. De Martini, "Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states," Phys. Rev. A 66, 033801 (2002).
[CrossRef]

M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
[CrossRef] [PubMed]

Roger, G.

A. Aspect, J. Dalibard, and G. Roger, "Experimental Test of Bell’s Inequalities using Time- Varying Analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982), among others.
[CrossRef]

Rosen, N.

A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Salles, A.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Schnabel, R.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
[CrossRef] [PubMed]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Shor, P. W.

P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A 52, R2493- R2496 (1995).
[CrossRef] [PubMed]

Silberhorn, C.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Simon, C.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
[CrossRef] [PubMed]

Skwara, P.

P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
[CrossRef]

Souto Ribeiro, P. H.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Steane, A. M.

A. M. Steane, "Error Correcting Codes in Quantum Theory," Phys. Rev. Lett. 77, 793-797 (1996).
[CrossRef] [PubMed]

Stoler, D.

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[CrossRef] [PubMed]

Takeno, Y.

Takeuchi, S.

H. F. Hofmann and S. Takeuchi, "Violation of local uncertainty relations as a signature of entanglement," Phys. Rev. A 68, 032103 (2003).
[CrossRef]

Tanas, R.

Z. Ficek and R. Tanas, "Dark periods and revivals of entanglement in a two-qubit system," Phys. Rev. A 74, 024304 (2006).
[CrossRef]

Toth, G.

G. Toth, "Entanglement detection in optical lattices of bosonic atoms with collective measurements," Phys. Rev. A 69, 052327 (2004).
[CrossRef]

Vahlbruch, H.

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

Vidal, G.

G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002).
[CrossRef]

Walborn, S. P.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Weller, A.

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

Werner, R. F.

G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002).
[CrossRef]

R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model," Phys. Rev. A 40, 4277-4281 (1989).
[CrossRef] [PubMed]

Wiseman, H. M.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Phys. Rev. Lett. 98, 140402 (2007).
[CrossRef] [PubMed]

Wooters, K.

K. Wooters, "Entanglement of Formation of an Arbitrary State of Two Qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).
[CrossRef]

Yonezawa, H.

Yu, T.

T. Yu and J. H. Eberly, "Sudden Death of Entanglement," Science 323, 598-601, (2009).
[CrossRef] [PubMed]

T. Yu and J. H. Eberly, "Finite-Time Disentanglement Via Spontaneous Emission," Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

Yukawa, M.

Yurke, B.

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[CrossRef] [PubMed]

Zeilinger, A.

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, "A wavelength-tunable fiber-coupled source of narrowband entangled photons," Opt. Express 15, 15377-15386 (2007).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Zurek, W. H.

W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715-775 (2003).
[CrossRef]

J. Mod. Opt.

E. G. Cavalcanti and M. D. Reid, "Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes," J. Mod. Opt. 54, 2373-2380 (2007).
[CrossRef]

Nature

B. Julsgaard, A. Kozhekin, and E. S. Polzik, "Experimental long-lived entanglement of two macroscopic objects," Nature 413, 400-403(2001).
[CrossRef] [PubMed]

J. Esteve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, "Squeezing and entanglement in a Bose-Einstein condensate," Nature 455, 1216-1219 (2008).
[PubMed]

Opt. Express

Phys. Lett. A

J. Larsson, "Modeling the singlet state with local variables," Phys. Lett. A 256, 245-252 (1999).
[CrossRef]

Phys. Rev.

A. Einstein, B. Podolsky and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
[CrossRef]

W. H. Furry, "Note on the Quantum-Mechanical Theory of Measurement," Phys. Rev. 49, 393-399 (1936).
[CrossRef]

Phys. Rev. A

H. F. Hofmann and S. Takeuchi, "Violation of local uncertainty relations as a signature of entanglement," Phys. Rev. A 68, 032103 (2003).
[CrossRef]

M. D. Reid, "Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification," Phys. Rev. A 40, 913-923 (1989).
[CrossRef] [PubMed]

M. D. Reid, W. J. Munro, and F. De Martini, "Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states," Phys. Rev. A 66, 033801 (2002).
[CrossRef]

P. Skwara, H. Kampermann, M. Kleinmann, and D. Bruss, "Entanglement witnesses and a loophole problem," Phys. Rev. A 76, 012312 (2007).
[CrossRef]

G. Toth, "Entanglement detection in optical lattices of bosonic atoms with collective measurements," Phys. Rev. A 69, 052327 (2004).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, "Polarization squeezing and continuousvariable polarization entanglement," Phys. Rev. A 65, 052306 (2002).
[CrossRef]

G. Vidal and R. F. Werner, "Computable measure of entanglement," Phys. Rev. A 65, 032314 (2002).
[CrossRef]

R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model," Phys. Rev. A 40, 4277-4281 (1989).
[CrossRef] [PubMed]

Z. Ficek and R. Tanas, "Dark periods and revivals of entanglement in a two-qubit system," Phys. Rev. A 74, 024304 (2006).
[CrossRef]

C. H. Bennett et al., "Mixed-state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
[CrossRef] [PubMed]

P. W. Shor, "Scheme for reducing decoherence in quantum computer memory," Phys. Rev. A 52, R2493- R2496 (1995).
[CrossRef] [PubMed]

Phys. Rev. D

A. Garg and N. D. Mermin, "Detector inefficiencies in the Einstein-Podolsky-Rosen experiment," Phys. Rev. D 35, 3831-3835 (1987).
[CrossRef]

N. D. Mermin, "Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s," Phys. Rev. D 22, 356-361 (1980).
[CrossRef]

Phys. Rev. Lett.

P. D. Drummond, "Violations of Bell’s Inequality in Cooperative States," Phys. Rev. Lett. 50, 1407-1410 (1983).
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A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, "Conditional preparation of single photons for scalable quantum-optical networking," Phys. Rev. Lett. 93, 093601 (2004).
[CrossRef] [PubMed]

H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen, N. Lastzka, S. Goler, K. Danzmann, and R. Schnabel, "Observation of Squeezed Light with 10-dB Quantum-Noise Reduction," Phys. Rev. Lett. 100, 033602 (2008).
[CrossRef] [PubMed]

A. M. Steane, "Error Correcting Codes in Quantum Theory," Phys. Rev. Lett. 77, 793-797 (1996).
[CrossRef] [PubMed]

B. Yurke and D. Stoler, "Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).
[CrossRef] [PubMed]

A. Aspect, J. Dalibard, and G. Roger, "Experimental Test of Bell’s Inequalities using Time- Varying Analyzers," Phys. Rev. Lett. 49, 1804-1807 (1982), among others.
[CrossRef]

W. P. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, "Polarization Squeezing of Continuous Variable Stokes Parameters," Phys. Rev. Lett. 88, 093601 (2002).
[CrossRef] [PubMed]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Phys. Rev. Lett. 98, 140402 (2007).
[CrossRef] [PubMed]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental Investigation of Criteria for Continuous Variable Entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum Superpositions of a Mirror," Phys. Rev. Lett. 91, 130401 (2003).
[CrossRef] [PubMed]

M. Barberi, F. De Martini, G. Di Nepi, and P. Matalon, "Generation and Characterization of Werner States and Maximally Entangled Mixed States by a Universal Source of Entanglement," Phys. Rev. Lett. 92, 177901 (2004).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

T. Yu and J. H. Eberly, "Finite-Time Disentanglement Via Spontaneous Emission," Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef] [PubMed]

A. Peres, "Separability Criterion for Density Matrices," Phys. Rev. Lett. 77, 1413-1415 (1996).
[CrossRef] [PubMed]

M. Horodecki, P. Horodecki, and R. Horodecki, "Mixed-State Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?," Phys. Rev. Lett. 80, 5239-5242 (1998).
[CrossRef]

K. Wooters, "Entanglement of Formation of an Arbitrary State of Two Qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).
[CrossRef]

Physics

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-201 (1965).

Rev. Mod. Phys.

W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715-775 (2003).
[CrossRef]

Science

T. Yu and J. H. Eberly, "Sudden Death of Entanglement," Science 323, 598-601, (2009).
[CrossRef] [PubMed]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, "Environment-Induced Sudden Death of Entanglement," Science 316, 579-582 (2007).
[CrossRef] [PubMed]

Other

D. Bohm, Quantum Theory (Englewood Cliffs, NJ, Prentice-Hall, 1951).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic diagram of Bohm’s EPR experiment with correlated spins at spatially-separated locations A and B.

Fig. 2.
Fig. 2.

Negativity of decohered Bell state to show entanglement sudden death for noise decoherence at p<1/3, but continuous suppression of entanglement for loss decoherence at all η.

Fig. 3.
Fig. 3.

(a) Threshold detection efficiency ηmin required (by (6)) to confirm entanglement and the spin EPR paradox via (3) and (4), for a given mean photon number 〈NB 〉.

Equations (13)

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ΨS=12(1A1B1A1B)
ρF=[η2ρW000(η/2)(1η)I4000(1η)2].
Δ2Jx+Δ2Jy+Δ2 Jz <NA+NB / 2 ,
Δinf2JxB+Δinf2JyB+Δinf2 JzB <NB/ 2 .
ψN=1N!N+1 (a+bab+)N 0.
H=ih̅ κ (a+bab+)ih̅κ(a+bab+).
a±=a± (0)cosh(r)±b(0)sinh(r)
b±=b± (0) cosh(r) a (0) sinh(r),
(JZA)2 =(1/2)η sinh2 (r)(1+ηsinh2(r))
JZAJZB=(1/2) η2 cos h2 (r)sinh2(r),
Δ2Jx=Δ2Jy=Δ2Jz=η (1η) sin h2 (r),
Δinf2JθB=(JθB)2JθBJθA2/(JθA)2
=ηsinh2r(1η2+2η(1η)sinh2r)2(1+ηsinh2r)

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